Edge universality for deformed Wigner matrices

J. Lee, K. Schnelli, Reviews in Mathematical Physics 27 (2015).


Journal Article | Published | English
Author
Department
Abstract
We consider N × N random matrices of the form H = W + V where W is a real symmetric Wigner matrix and V a random or deterministic, real, diagonal matrix whose entries are independent of W. We assume subexponential decay for the matrix entries of W and we choose V so that the eigenvalues of W and V are typically of the same order. For a large class of diagonal matrices V, we show that the rescaled distribution of the extremal eigenvalues is given by the Tracy-Widom distribution F1 in the limit of large N. Our proofs also apply to the complex Hermitian setting, i.e. when W is a complex Hermitian Wigner matrix.
Publishing Year
Date Published
2015-09-01
Journal Title
Reviews in Mathematical Physics
Volume
27
Issue
8
Article Number
1550018
IST-REx-ID

Cite this

Lee J, Schnelli K. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 2015;27(8). doi:10.1142/S0129055X1550018X
Lee, J., & Schnelli, K. (2015). Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics, 27(8). https://doi.org/10.1142/S0129055X1550018X
Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics 27, no. 8 (2015). https://doi.org/10.1142/S0129055X1550018X.
J. Lee and K. Schnelli, “Edge universality for deformed Wigner matrices,” Reviews in Mathematical Physics, vol. 27, no. 8, 2015.
Lee J, Schnelli K. 2015. Edge universality for deformed Wigner matrices. Reviews in Mathematical Physics. 27(8).
Lee, Jioon, and Kevin Schnelli. “Edge Universality for Deformed Wigner Matrices.” Reviews in Mathematical Physics, vol. 27, no. 8, 1550018, World Scientific Publishing, 2015, doi:10.1142/S0129055X1550018X.

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